A study due out in the July 8 issue of the American Journal of Clinical Nutrition found just that. Researchers tested the cholesterol response in identical twins (with identical genes), and found their levels were about the same - even though one exercised regularly while one was relatively sedentary, even though one ate a low-fat diet while the other ate a high-fat one.
Lifestyle matters, but it's always a good idea to monitor and manage your lipid levels with your healthcare provider.
For a summary of the study:
Bad Cholesterol: Genes Make the Difference
For the study itself:
Concordant lipoprotein and weight responses to dietary fat change in identical twins with divergent exercise levels